Question

What is the median nighttime charge for 360 minutes of calling?

• A. $63.84
• B. $71.40
• C. $72.50
• D. $87.92
• E. $113.29
• A. 7%
• B. 14%
• C. 28%
• D. 33%
• J. 40%

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
The median is the middle value in a set of numbers arranged in ascending order. In this problem, we are asked to find the median of the \textit{nighttime charges} from the bar chart for five phone services (P, Q, R, S, T). This involves reading the nighttime charges, sorting them, and identifying the middle value. Step 2: Key Approach:
1. Identify the nighttime charges (dark bars) for each service. 2. Arrange the charges in ascending order. 3. Since there are five values, the median is the 3rd value in the sorted list. Step 3: Detailed Calculation:
From the bar chart, the nighttime charges are: \[ \text{P: } $50.10,
\text{Q: } $52.89,
\text{R: } $72.50,
\text{S: } $72.31,
\text{T: } $71.40 \] Sorting these charges in ascending order: \[ 50.10,
52.89,
71.40,
72.31,
72.50 \] For a list of 5 numbers, the median is the 3rd value: \[ \text{Median} = 71.40 \] Step 4: Verification and Reasoning:
- The sorted list clearly shows $71.40 is the middle value. - Cross-checking the bar chart confirms the values: P and Q are lower, T, S, and R are higher, so 71.40 is indeed the middle. - The answer key lists $72.50 as the median. However, based on standard statistical definition, the median of the five nighttime charges is $71.40. - Therefore, either the question contains a labeling error or the answer key is incorrect. Step 5: Final Answer:
\[ \boxed{$71.40} \] This solution logically identifies the median by following the definition and carefully checking the data from the bar chart.

Answer 2

Step 1: Understanding the Concept:
This question asks for the percent increase from the nighttime charge to the daytime charge for phone service T.
Step 2: Key Formula or Approach:
The formula for percent increase is: \[ \text{Percent Increase} = \frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \times 100% \] Here, the "New Value" is the daytime charge, and the "Original Value" is the nighttime charge.
Step 3: Detailed Explanation:
First, we need to read the charges for phone service T from the bar chart.

Daytime charge (light bar) for T: $99.40
Nighttime charge (dark bar) for T: $71.40
The "Original Value" (the value we are comparing to) is the nighttime charge, $71.40. The "New Value" is the daytime charge, $99.40. First, find the amount of the increase: \[ \text{Increase} = $99.40 - $71.40 = $28.00 \] Now, use the percent increase formula: \[ \text{Percent Increase} = \frac{$28.00}{$71.40} \times 100% \] To approximate this calculation: \[ \frac{28}{71.4} \approx \frac{28}{70} = \frac{4 \times 7}{10 \times 7} = \frac{4}{10} = 0.4 \] Converting the decimal to a percentage: \[ 0.4 \times 100% = 40% \] Let's check with a slightly more precise calculation: \(28 / 71.4 \approx 0.392\). This is very close to 40%.
Step 4: Final Answer:
The daytime charge is approximately 40% more than the nighttime charge for service T.